Jacob, the son of Isaac and Rebecca and the grandson of Abraham and Sarah, is one of the most important biblical characters. According to the Book of Genesis, he was the third Hebrew progenitor with whom God made a covenant and was later given the name Israel. Among many of his famous stories mostly mentioned in Bible, there is an interesting account of a ladder which was (a sort of) bridge between the earth and heavens. The story tell us that while on a journey, he slept and saw a staircase in dream, top of which reached to heavens. The exact account goes as follows,
“……And he dreamed, and behold, there was a ladder set up on the earth, and the top of it reached to heaven; and behold, the angels of God were ascending and descending on it! And behold, the Lord stood above it [or “beside him”] and said, “I am the Lord, the God of Abraham your father and the God of Isaac……” (Genesis 28:10-19).
Apart from all metaphorical and religious descriptions and commentaries, to me, Jacob’s Ladder is an expression of man’s long-lasting dream to reach heavens and his inherent quest to explore what is unknown. This ladder is our journey from what we know, towards what we don’t know. This narrative device is not the only historical reference mentioning a built structure high-enough to reach heavens. You can also find similar descriptions in Greek and Indian mythologies. From ancient times, the desire to raise high, being more close to God and to know what lies beyond skies, was always a hallmark of human curiosity. So how much high we could go, from Jacob’s time till now? His ladder was imaginary and figurative but in reality, how high we could build after him? An excellent attempt to answer this question and providing a brief history of an ever-continuing competition to build the tallest structure, can be seen in the following video.
But hold on!!! Can the size of a structure be increased indefinitely for it to be able to carry its own weight? How long a bar of uniform cross-section can be, before it breaks due to its own weight? The first person who attempted to answer this question was Galileo Galilei (1654 AD – 1642 AD) who introduced the concept of “Specific Strength” of a material. It simply states that there exists an absolute limit to the length that a bar can attain without breaking under its own weight. Larger a structure is, larger is the proportion of its own weight to the total load which it can carry. For structures subjected to any loading (other than self-weight), as the size increases, its strength increases with the square of the ruling dimensions, while the weight increases with its cube. It means increasing the cross sectional area doesn’t always help in making the structure strong. For example, simply increasing the slab thickness may not help in avoiding punching shear failure, as the shear force is also increased because of additional self-weight. So depending upon the type and geometry of structure, there exists a maximum possible size beyond which it cannot carry even its own weight. The Specific Length of a simple bar (corresponding to Specific Strength) can be easily determined by equating the weight of the bar to its tensile strength. This concept makes it impossible to construct structures of enormous size using known materials to date. Natural structures (trees, mounds, animals, etc.) also have a size limit. An interested observation is that proportions of aquatic animals are almost unaffected by their size because their weight is almost entirely supported by buoyancy.
Another application of specific strength concept is in the aircraft manufacturing industry. Aircrafts, in addition of external loads, must be capable of being raised into the air under their own weight, requiring the usage of materials with high specific strength. Wood has a high specific strength especially in tension and was extensively used in early planes. Various aero-modeling clubs use Balsa wood (because of its high specific strength) to make model planes. Similarly, in wind tunnel testing, building models are often made using lightweight Balsa wood to minimize the effects of heavy mass. Long bridges (with span length > 50 m) are mostly designed to carry only their own weight. The live load (vehicle loadings) is only a small proportion compared to the self-weight of bridge. As we are advancing towards more efficient structural systems, we are looking for materials with high specific strength (i.e. materials that are very light yet can withstand large amount of applied loading). Example of such ultra-strong materials include carbon fibers and carbon nanotubes.
So the race is always on. The limitations and controlling factors that stop towers from rising ever-higher can be classified under materials, physical human comfort, elevator technology and, most importantly, economy. The Council on Tall Buildings and Urban Habitat (CTBUH) (an association consisting of world-renowned experts on design of tall buildings) recently asked a group of leading skyscraper architects and designers about some of the controlling factors limiting the height of tall buildings. The question was, “What do you think is the single biggest limiting factor that would prevent humanity creating a mile-high tower or higher?” Their responses can be seen in the following video.
Our dreams will keep on leading us to higher and higher structures. The race is not going to stop, at least in near-future. Innovative ideas e.g. space elevator (just google it), are nowadays fascinating us just like the desire to land on moon once fascinated us. Our today’s dreams suggest us that one day, in reality, we may be able to step on Jacob’s Ladder.